Linear vs Exponential Worksheets Grade 9

1. Noah is comparing two different investment accounts for his summer internship earnings. Account A starts with an initial deposit of $6,000 and adds a fixed amount of $360 each year. Account B starts with an initial deposit of $6,000 and grows by 6% each year, compounded annually. Write functions A(t) and B(t) to model the balance in each account after t years. Identify which account represents linear growth and which represents exponential growth, and explain the key difference in how the balances change over time.
2. A city planner is analyzing two different investment strategies for a municipal project. Strategy A grows according to the function A(t) = 5000 + 300t, where t is time in years. Strategy B grows according to the function B(t) = 4000 × (1.08)^t. The planner needs to determine which strategy represents exponential growth and which represents linear growth. Which statement correctly identifies the growth types?
3. Aroha is analyzing two functions displayed on a coordinate grid. The first function, f(x), passes through the points (1, 9) and (3, 81). The second function, g(x), passes through the points (1, 9) and (3, 15). For each function, as x increases by 2 from x = 1 to x = 3, determine whether the function is linear or exponential. Justify your answer by describing the pattern of change in y.

…and 3 more problems

1. 2^(x+3) = 32
2. Emma plots two functions on the same coordinate grid. Function A passes through the points (0, 10) and (1, 15). Function B passes through the points (0, 10) and (1, 20). For x = 0 to x = 4, which function grows faster and why? Identify whether each function is linear or exponential, and explain how you can tell from the graph.
3. Emma is comparing two different savings accounts for her summer job earnings. Account A earns simple interest, adding $75 each year to her initial deposit of $1,125. Account B earns compound interest at a rate of 5% per year, applied to the total balance each year, starting from the same initial deposit of $1,125. Write functions A(t) and B(t) to model the balance in each account after t years. Determine which account is linear and which is exponential, and calculate the balance in each account after 7 years to the nearest dollar. Which account has a higher balance after 7 years, and by how much?

…and 3 more problems

1. Aroha compares two functions: f(x) = 9x + 3 and g(x) = 9(3)^x. For x = 0, 1, 2, 3, which function grows faster and why?
2. Sophia is comparing two different investment accounts for her college fund. Account A starts with $6,000 and adds $360 each year. Account B starts with $6,000 and grows by 6% each year, meaning the balance is multiplied by 1.06 each year. Write functions A(t) and B(t) to model the balance in each account after t years. Determine which account represents linear growth and which represents exponential growth, and explain the difference in their growth patterns. Then calculate the balance in each account after 6 years, and state which account has a higher balance and by how much.
3. A research scientist is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and the population doubles every 3 hours. Liam needs to determine the bacterial population after 9 hours. Write an exponential function to model this growth and calculate the population after 9 hours.

…and 3 more problems